Large N behavior of two dimensional supersymmetric Yang-Mills quantum mechanics

TL;DR

This paper investigates the large N limit of two-dimensional supersymmetric Yang-Mills quantum mechanics, revealing the importance of bilinear operators alongside single trace operators in the system's description.

Contribution

It introduces SU(N) invariant polynomials to solve 2D SYMQM and shows the significance of bilinear operators in the large N limit.

Findings

Large N limit analyzed for 2D SYMQM

Bilinear operators are crucial in the free Hamiltonian case

Solutions expressed in terms of SU(N) invariant polynomials

Abstract

We analyze the $N \to \infty $ limit of supersymmetric Yang-Mills quantum mechanics (SYMQM) in two spacetime dimensions. To do so we introduce a particular class of SU(N) invariant polynomials and give the solutions of 2D SYMQM in terms of them. We conclude that in this limit the system is not fully described by the single trace operators $Tr({a^{\dagger}}^n)$ since there are other, bilinear operators $Tr^n(a^{\dagger}a^{\dagger})$ that play a crucial role when the hamiltonian is free.